Bohrs Theory

Copyright 2005, 1999, 1991 by The McGraw-Hill Companies, Inc. Click here for terms of use. 

Only electron transitions down to the second orbit cause emission of visible light. Other transitions may involve infrared or ultraviolet light. 

The electrons in atoms other than hydrogen also occupy various energy levels. With more than one electron in each atom, the question of how many electrons can occupy a given level becomes important. The maximum number of electrons that can occupy a given shell depends on the shell number. For example, in any atom, the first shell can hold a maximum of only 2 electrons, the second shell can hold a maximum of 8 electrons, the third shell can hold a maximum of 18 electrons, and so forth. The maximum number of electrons that can occupy any particular shell is 2n, where n is the shell number. 

EXAMPLE 4.1. What is the maximum number of electrons that can occupy the N shell  

The N shell in an atom corresponds to the fourth energy level (n = 4) hence the maximum number of electrons it can hold is 

---

To make an informed guess for your first value of ot, you may wish to reread the section on the Bohr theory of the hydrogen atom and the Schroedinger wave functions for the hydrogen atom in a good physical or general chemistry book (see Bibliography). 

Hafinia, Latin name for Copenhagen) Many years before its discovery in 1932 (credited to D. Coster and G. von Hevesey), Hafnium was thought to be present in various minerals and concentrations. On the basis of the Bohr theory, the new element was expected to be associated with zirconium. 

The functions are known as the angular wave functions or, because they describe the distribution of p over the surface of a sphere of radius r, spherical harmonics. The quantum number n = l,2,3,...,oo and is the same as in the Bohr theory, is the azimuthal quantum number associated with the discrete orbital angular momentum values, and is... 

Unlike the total energy, the quantum mechanical value Pi of the orbital angular momentum is significantly different from that in the Bohr theory given in Equation (1.8). It is now given by... 

Moseley photographed characteristic spectra for some 38 elements that could serve as x-ray tube targets. In two papers,37 he not only uncovered structure in the K and L spectra—he alscr established the atomic number as more fundamental than the atomic weight, and he provided brilliant support for- the Bohr theory of atomic structure. 

These energy levels agree with the values obtained in the earlier Bohr theory. 

Bohr theory, the radius of the circular orbit of the electron in the ground state of the hydrogen atom (Z = 1) with a stationary nucleus. Except in Section 6.5, where this substitution is not appropriate, we replace fx by and by ao in the remainder of this book. 

Draw a picture of the electron jump corresponding to the first line in the visible emission spectrum of hydrogen according to the Bohr theory. 

Bohr theory the first theory of atomic structure which involved definite internal energy levels for electrons. 

The carbon atom has, outside its nucleus, six electrons which, on the Bohr theory of atomic structure, were believed to be arranged in orbits at increasing distance from the nucleus. These orbits corres-... 

The Bohr theory also permits a calculation of the total energy, E, of the atom from Hamilton s equation ... 

This section started with the discovery of Soddy and Fajans on radioactive decay around 1910 and the relationship of radioactive decay to the periodic table. At this point in the history, we understand the periodic table and we understand the role of isotopes in the periodic table. We have not yet understood the structure of the modern Table, i.e. first row two elements, second row eight elements, etc. That understanding can be based on Bohr theory of the hydrogen atom originally developed in 1911 and is summarized in Bohr s famous article in Zeitschrift fur Physik (Bohr 1922). 

It has already been noted that the new quantum theory and the Schrodinger equation were introduced in 1926. This theory led to a solution for the hydrogen atom energy levels which agrees with Bohr theory. It also led to harmonic oscillator energy levels which differ from those of the older quantum mechanics by including a zero-point energy term. The developments of M. Born and J. R. Oppenheimer followed soon thereafter referred to as the Born-Oppenheimer approximation, these developments are the cornerstone of most modern considerations of isotope effects. 

The Bohr theory of atomic structure allotted to each extra-nuclear electron within the atom a definite geometrical orbit and, more important, associated with each orbit a fixed total energy value. 

As indicated, these problems can be eliminated consistently within Bohr theory, where a nonnegative expression for Lq or Lo , valid approximately down to... 

Dipole oscillator strengths form important input into all stopping models based on Bethe or Bohr theory. Emphasis has frequently been on total /-values which show only little sensitivity to the specific input. More important are differential oscillator-strength spectra, in particular at projectile speeds where inner-shell excitation channels are closed. Spectra bundled into principal or subshells [60] are sufficient for many purposes, but the best available tabulations are based on analysis of optical data rather than on theory, and such data are unavailable for numerous elements and compounds [61]. 

The dependence of the elastic pressure on the density can be expressed approximately by a power function p = Bpn, usually called polytropic. It could alternatively be considered that the force centers are repelled according to the relationship F = a/(3n-2) as assumed in the Bohr theory of crystal lattices. The thermal motion, at this degree of compression, consists of small oscillations. To each vibrational degree of freedom there corresponds an energy RT (per mole). The total oscillatory energy equals cvT, where cv is independent of the volume in this approximation... 

Figure 8. A Bohr-Sommerfeld model of the xenon atom. (From H. A. Kramers and H. Horst, The Atom and the Bohr Theory of its Structure, 1924).

It was the apparent violation of this requirement that led to the postulate of quantization in the Bohr theory of the hydrogen atom. However, we are concerned here with the classical result in which the charge does radiate. Our objective is to describe the emitted radiation some distance r from the emitter. 

A more detailed account of the Bohr theory of the hydrogen atom is given in Chap. 2 and Apps. II and III. 

The quantity a0 is interpreted in the Bohr theory as the radius of the smallest orbit in the hydrogen atom its value is 0.530 A. 

---